Renewed bickering between the duo has emerged from comments Ponting made in his new autobiography and threatens to overshadow the lead-up to the Ashes.
In his book, At the Close of Play, Ponting has offered a less than favourable appraisal of Clarke, in particular his attitude under him as vice-captain and his ill-fated soap opera relationship with Lara Bingle.
Arthur was national team coach from 2011 until his sacking just before this year's Ashes series in England and admitted he was aware of the bad blood.
"It was just a sign of the times really," he told 6PR.
"When you are in an evolving team, there is a lot of that that goes on because guys are insular and guys are insecure.
"We just needed to string some good performances together to gain confidence. Then guys feel comfortable around their team-mates and that's we were trying to achieve."
Arthur said he was confused by a chapter in Ponting's book that said Arthur wasn't the right fit as Australian coach his appointment was the result of muddled thinking from Cricket Australia.
"Our relationship was always quite good," Arthur said.
"One thing I know about Ricky is that he will always speak his mind. He was honest and straight to point. That was one thing I always appreciated with Ricky.
"I'm looking forward to having a chat with him."
Arthur also revealed that Clarke instigated an emotional tribute to Ponting in the WACA Ground dressing rooms immediately after his retirement in the Perth Test last summer.
He said Clarke stood in front of the team and paid homage to 'what Ponting meant to him' which led Arthur to believe that their previously strained relationship had been mended.
"The team gave Ricky a massive present and Michael was the one who handed it over. And Michael gave a speech from the heart that was unbelievable. It had the whole dressing room in tears," Arthur said.
Arthur was due to attend a leadership breakfast at Perth's Crown Casino on Wednesday where Ponting was to perform as a key guest speaker.
"I have already been on the line to Ricky and he knows I'm coming in. I didn't want him abusing me if I was in the audience," Arthur said light-heartedly.